Geodesic
Hyperidentities in many-sorted algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 1, pp. 47-74.

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The theory of hyperidentities generalizes the equational theory of universal algebras and is applicable in several fields of science, especially in computers sciences (see e.g. [2,1]). The main tool to study hyperidentities is the concept of a hypersubstitution. Hypersubstitutions of many-sorted algebras were studied in [3]. On the basis of hypersubstitutions one defines a pair of closure operators which turns out to be a conjugate pair. The theory of conjugate pairs of additive closure operators can be applied to characterize solid varieties, i.e., varieties in which every identity is satisfied as a hyperidentity (see [4]). The aim of this paper is to apply the theory of conjugate pairs of additive closure operators to many-sorted algebras.
Keywords: hypersubstitution, hyperidentity, heterogeneous algebra 
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Denecke, Klaus; Lekkoksung, Somsak. Hyperidentities in many-sorted algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 1, pp. 47-74. http://geodesic.mathdoc.fr/item/DMGAA_2009_29_1_a3/

[1] P. Baltazar, M-Solid Varieties of Languages, Acta Cybernetica 18 (2008) 719-731.

[2] K. Denecke and S. L. Wismath, Hyperidenties and Clones, Gordon and Breach, 2000.

[3] K. Denecke and S. Lekkoksung, Hypersubstitutions of Many-Sorted Algebras, Asian-European J. Math. Vol. I (3) (2008) 337-346.

[4] J. Koppitz and K. Denecke, M-solid Varieties of Algebras, Springer 2005.

[5] H. Lugowski, Grundzüge der Universellen Algebra, Teubner-Verlag, Leipzig 1976.